Rational continuity: parametric, geometric, and Frenet frame continuity of rational curves
- 1 October 1989
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 8 (4), 335-359
- https://doi.org/10.1145/77269.77274
Abstract
The parametric, geometric, or Frenet frame continuity of a rational curve has often been ensured by requiring the homogeneous polynomial curve associated with the rational curve to possess either parametric, geometric, or Frenet frame continuity, respectively. In this paper, we show that this approach is overly restrictive and derive the constraints on the associated homogeneous curve that are both necessary and sufficient to ensure that the rational curve is either parametrically, geometrically, or Frenet frame continuous.Keywords
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